Structure superposition and RMSD calculations.

Methods for superimposing atomic structures. More...

Functions
template<typename AtomIterator1, typename AtomIterator2>
double	leastsquares_superposition (AtomIterator1 fixed_first, AtomIterator1 fixed_last, AtomIterator2 superimpose_first, AtomIterator2 superimpose_last, BTK::MATH::BTKMatrix &U, BTK::MATH::BTKVector &T)
	Calculate the transformation resulting in the least-squares superposition of two atom sets.
template<typename AtomIterator1, typename AtomIterator2, typename AtomIterator3>
double	leastsquares_superposition (AtomIterator1 fixed_first, AtomIterator1 fixed_last, AtomIterator2 superimpose_first, AtomIterator2 superimpose_last, AtomIterator3 transform_first, AtomIterator3 transform_last)
	Applies the least-squares superposition of two atom sets to a third atom set.
template<typename AtomIterator1, typename AtomIterator2>
double	get_rmsd (AtomIterator1 a1_first, AtomIterator1 a1_last, AtomIterator2 a2_first, AtomIterator2 a2_last)
	Calculate the superimposed RMSD of two atom sets.
template<typename AtomIterator1, typename AtomIterator2>
double	get_trivial_rmsd (AtomIterator1 a1_first, AtomIterator1 a1_last, AtomIterator2 a2_first, AtomIterator2 a2_last)
	calculate the trivial (non-superimposed) RMSD between two atom sets.

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Detailed Description

Methods for superimposing atomic structures.

These are iterator-based methods for optimally superimposing atomic structures, computing the RMSD between atomic structures, or both. For more information on the theory behind these methods, see this discussion of the mathematics of RMSD.

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Function Documentation

double BTK::ALGORITHMS::get_rmsd	(	AtomIterator1	a1_first,
		AtomIterator1	a1_last,
		AtomIterator2	a2_first,
		AtomIterator2	a2_last
	)

Calculate the superimposed RMSD of two atom sets.

This method computes the optimal superposition of all atoms in the range [a1_first,a1_last) to all atoms in the range [a2_first,a2_last), and returns the RMSD value between the superimposed atoms. If the two sets of atoms are of unequal size, the calculation will be performed over the number of atoms in the smaller set.

double BTK::ALGORITHMS::get_trivial_rmsd	(	AtomIterator1	a1_first,
		AtomIterator1	a1_last,
		AtomIterator2	a2_first,
		AtomIterator2	a2_last
	)

calculate the trivial (non-superimposed) RMSD between two atom sets.

Same as get_rmsd(), but sets [a1_first,a1_last) and [a2_first,a2_last) are not superimposed prior to the RMSD calculation.

double BTK::ALGORITHMS::leastsquares_superposition	(	AtomIterator1	fixed_first,
		AtomIterator1	fixed_last,
		AtomIterator2	superimpose_first,
		AtomIterator2	superimpose_last,
		AtomIterator3	transform_first,
		AtomIterator3	transform_last
	)

Applies the least-squares superposition of two atom sets to a third atom set.

Applies the least squares transformation of atom set 'superimpose' onto atom set 'fixed' to atom set 'transform'.

Returns:

The RMSD between atom sets 'superimpose' and 'fixed'.

double BTK::ALGORITHMS::leastsquares_superposition	(	AtomIterator1	fixed_first,
		AtomIterator1	fixed_last,
		AtomIterator2	superimpose_first,
		AtomIterator2	superimpose_last,
		BTK::MATH::BTKMatrix &	U,
		BTK::MATH::BTKVector &	T
	)

Calculate the transformation resulting in the least-squares superposition of two atom sets.

Calculates the least-squares superposition of two sets of atoms using the method of Kabsch (Acta Cryst., 1978. A34, 827-828).

The transformation of the second atom set to the superimposed position can be recreated from the rotation matrix and the translation vector by

Parameters:

	U	After return, contains the superposition rotation matrix.
	T	After return, contains superposition translation vector.
	rmsd	After return, contains the RMSD of the superimposed sets.

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